It would be helpful to know your coordinates. A certain difference in latitude would be helpful for the measurements. Plus, if you don't want to be restricted to measurements at the sun's culmination, the difference in longitude is necessary for the calculations of the time.

Eratosthenes measured the angle of the sun at local noon in two places. If the points are not at the same longitude you do not want the measurements to be at the same universal time. It's important that it is true local noon, i.e. when the sun is at its highest.
You will also need to know how much further south one point is than the other. If there is a large difference in longitude that might be tricky. Depending exactly where in France you are, your best bet might be to collaborate with someone in Spain.

And just to be clear "local noon" in this context does not mean noon as displayed on your clock or wristwatch. "Local noon" can be quite a bit different than what your clock says depending on where your location is within your time zone. It will probably be within +/- 30 minutes from what your clock says noon is. But +/- 30 minutes off can be a big source of error here.

You could use the Internet to find out where your local noon is (based on your particular location and time zone).

However, if you want to do this experiment with pizazz, I suggest using a sun-dial to give you your local noon. The person you collaborate with should also use a sun-dial to find their local noon (which might be different than yours).

Each of you should calibrate your respective sun-dials such they actually point toward Celestial North. Ensuring it lines up with Polaris, the North Star, should suffice for this experiment. (Don't use magnetic North, btw. Magnetic deviation and variation can also be sources of error.) Certainly do not use a sun-dial that was just set up for decoration and isn't Aligned to true North.

Once the sundials are calibrated (aligned to True North), measurements should be performed at your own local noon according to your respective sun-dials (your measurement at your local noon, and you partner's measurement at their local noon.)

"local noon" in this context does not mean noon as displayed on your clock

Yes, I did point that out in post #3, but omitted to describe how to find it, working from scratch, as E would have done.
Using a plumb line, erect a vertical pole in a flat horizontal area. Mark a circle around it at a radius somewhat less than the maximum expected length of the shadow ( if unsure, mark several). As the day progresses, the tip of the shadow will cross these circles. Mark each such point. Join the two points where each circle is crossed and bisect these lines to obtain true north. Next day, mark where the shadow crosses that bisecting line.

Thanks a lot for all the answers, we tried to understand them all We came to understand that the longitude is not usefull if we use the local noon. So here's our local noon. Please send yours and indicate us if you are interested in doing the experiment with us.

We do not need to know each others' local noons. In fact, you do not even need to know when your own local noon is according to the clock. As I wrote in post #10, you just need to take the shadow measurement when the sun as it its highest, i.e. when the shadow is shortest.
Using a published table to know when that is by the clock is a bit cheating. It depends how authentic you want to be.

The remaining problem is knowing the distance in the north-south direction between the two points. Again, you could do it by knowing the latitudes and working it out from there, but that really is cheating because it depends on knowing the radius of the Earth!
Looking at your location, you need someone in N France (Paris would be fine) or Belgique etc., somewhere where it would be reasonable to know the overland distance by direct measurement. I'm in Sydney, so definitely unsuitable.

I see you live in a beautiful part of the world. My wife and I cycled from Albi to St Remy de Provence once. Our overnight stays included Ganges and Sommieres.

(Warning! The error of my measurement may be quite high. I'm guessing ≈ ± 0.03 meters, as I wasn't expecting the sun to come out here for another 6 months, and it was cold, and the wind was blowing, and it would have taken me too much time fix things to reduce the error, to get a more accurate reading.)

Thank you a lot for all of your answers that we weren't expecting. We will use them.
We don't have much time so we think we are going to use all of our ressources just as Eratosthenes did with the repported informations he had on the distance between Alexandria and Syene.. Considering we are "cheating" would it be a problem to only use many photography or measurment from people around the world (who must speak english because it's necessary for our project)? Please send yours if you want and can. If we are not doing it the good way please explain us with more simple words.

And we do live in a beautiful country but so are the United-Kingdom and Sydney!

We are doing the experiment on the next monday (Monday the 27th) if you could spend a few minutes of your time to help us it would be very nice.

Thank you a lot

Experiment #1

I have a post on my front porch that is about 1 meter tall. This porch is on the south side of my house. The post is about 2 meters away from the front of my house.
Things which confounded my measurements:

1. The post is about a hands height too short of a meter.
2. The post is/was too close to the house to get a shadow on the edge of the deck.
3. The post is not vertical. (I'm a very bad carpenter)
4. Measurement was made with a very floppy steel tape measure.
​

I think the error may be even greater than I expressed earlier.​

Experiment #2

I decided that since my deck railing is very odd, I would modify the experiment to not require something exactly 1 meter in height, but use maths instead.
Things which I think confounded those measurements:

1. I used my eyeballs, instead of a rock on the end of a string to decide what was "vertical"
2. I also don't know how level my deck is.​

Experiment #3

Since I have a bunch of trees growing due south of my house, and couldn't get a shadow on my front porch at the right time, I decided to borrow the next door neighbors driveway. (He wasn't home.) I also have a free standing coat rack that is about 2 meters tall. I'm thinking the taller the stick, the less error we are going to get.
Things I think confounded those measurements:

1. I don't think his driveway is level.
2. The neighbors next to him came out, caught me, and gave me some very strange looks. They did not ask why I had put a coat rack in our mutual neighbors driveway. This disturbed me quite a bit, as normal people don't normally go around putting coat racks in their neighbors driveway. So I gathered all my equipment, and hurried home.​

It is currently raining, and I do not expect to see the sun at a useful time in the near future.

Things I would recommend:

1. Get the longest stick possible to create your shadow.
2. Make sure the ground is level. The only way I know how to do this is to put the stick at the south end of a pond. (Preferably shallow)
3. Use a rock at the end of a string to find out if your stick is vertical.
4. Have two other people available. Two to hold the measuring string, and one to write down the length of the shadow. (Wait! There are three of you. Perfect!)
5. Start taking measurements tomorrow, and see how much the shadow shrinks each day. Although I'm very near your latitude, I'm about 1/3 of the earth away from you in longitude, and I think my measurements will be off by quite a bit. (If the sun ever comes out, and I make myself a pond, and find someone to hold the other end of the measuring string, that is.)
​

Those are good ideas @OmCheeto. But one additional recommendation to that method is to repeat measurements throughout the midday of the given day in order to find one's local noon; the shortest shadow of that given day will correspond to the measurement at local noon*.

*(This assumes that stick is vertical [tested with a plumb line (i.e., a rock on a string)] and the surface is horizontal [a bubble level should probably suffice for verification].)

[Edit: or just look up your specific local noon on the Internet if you want to take a shortcut.]